it sure is a big change from 1966 to 1967 no matter when exactly the songs were pulled from for this band.
Going from covers to open ended free for all jams.
It is a major paradigm shift to say the least in what your local rock and roll band is playing.
This music is flashback inducing...

After a close comparison, the mysterious studio Smokestack Lightning is simply the 11/19/66 live version again, but in mono, slowed-down, and faded-out early.
(The same 11/19/66 Smokestack can also be found masquerading as a "2/12/67" studio take.)

The Lovelight is also not from the fall '67 Anthem sessions. It's the longest take from the Lovelight rehearsal session, which was commonly dated 11/19/67. That date is flagrantly wrong, though. After listening to the full rehearsal session, these Lovelights are clearly earlier & more primitive than even the 8/5/67 live version, which is much stronger and more fully developed.
In this studio take, the band are still working out the basic parts - Pigpen sings it a bit differently, Jerry's still figuring out his soloing, and a lot of the sections of the live Lovelights are still missing. So I would guess that the Lovelight session may have taken place in July '67 or so.

The Other One & Alligator>Caution remain safely in the mid-October '67 sessions. Alligator has the drum break that was added after Mickey Hart joined, so it's after 9/29. The Other One sounds stodgy & tentative compared to the live 10/22/67 version, so I think it precedes that.

A better studio take of the Other One suite from these sessions has surfaced as a filler track in this February '71 studio rehearsal:
http://archive.org/details/gd1971-02-01.sbd.Studio.Rehearsal.120486.flac16

Jammed on this Smokestack at Vassar College in 1980.....lit it up with old friends and crew....played it back a million times and never heard a better version.....30 Years Later! Outragious....

It's possible portions of this recording were used on Anthem, though I haven't studied it closely enough.

The Other One is slow and mellow, and Lovelight is has a lot of repetitive vamping.
I'm not sure that SmokeStack Lighting is from these sessions. It sounds like those from the 1966 shows. It's good, but unfortunately cut off before halfway through.

The first half of Alligator is the rhythmic skeleton of what is on Anthem, (PigPen not audible), but Jerry kicks in on the second half. I like this Caution, with PigPen clear and upfront, ending with a quick decent into feedback, timed to fit on the LP.

The limitation of the 22-minute vinyl LP side were what constricted Anthem of the Sun. The songs are similar in length and structure to the 10/20/67 Anthem studio (and on Anthem of the Sun itself). This session is more interesting, with somewhat better audio. The other Anthem session is here:
http://www.archive.org/details/gd67-10-20.studio.poynton-sirmick.85631.sbeok.flac16